Predatory Exclusive Dealing

Transcription

1 Predatory Exclusive Dealing Joachim Klein y Hans Zenger z March 23, 2010 Abstract While the previous literature on exclusive dealing has been concerned with the question of how exclusive dealing can raise static pro ts, this paper analyzes the question of how exclusive dealing can be used to predate in a dynamic context. It is shown that exclusive dealing may arise even if it reduces static pro ts. Exclusivity provisions may not only allow excluding e cient competitors, but indeed are often a cheaper exclusionary tool than predatory pricing. This is the case either if the prey s access to nance is not too limited, or if the predator has su ciently strong market power vis-à-vis the prey. JEL classi cation: K21, L11, L12, L41, L42 Keywords: exclusive dealing, predation We would like to thank Monika Schnitzer, Andreas Hau er, Sven Rady, Damien Neven, Giulio Federico and Ray Rees for valuable comments and suggestions. We are grateful to seminar participants in Munich, at the International Industrial Organization Conference in Boston, at the European Association for Research in Industrial Economics in Ljubljana and at the European Association of Law and Economics in Rome for helpful comments. Financial support from Deutsche Forschungsgemeinschaft through GRK 801 is gratefully acknowledged. The views expressed in this paper are those of the authors and do not necessarily re ect the views of DG Competition or the European Commission. y Munich Graduate School of Economics, University of Munich, Kaulbachstr. 45, D Munich, Germany, joachim.klein@lrz.uni-muenchen.de z European Commission, Chief Economist Team, Directorate-General for Competition, 1000 Bruxelles, Belgium, hans.zenger@ec.europa.eu. 1

2 1 Introduction The Chicago School s critique of antitrust action against exclusive dealing is based on the argument that, under the assumptions of those models, exclusive dealing is not pro table for rms in the absence of e ciencies like the protection of prior investments (see, for instance, Bork, 1978). From this it was concluded that exclusive dealing must be bene cial for welfare because it is only pro table for rms if there is an e ciency rationale. 1 The subsequent literature has shown, however, that exclusive dealing may be anticompetitive if the implicit assumptions of the Chicago School are relaxed. Much of this literature has focused on the exclusion of potential entrants. Exclusive dealing is often pro table in this case because potential entrants are assumed not to be in the position of making countero ers at the time the exclusive contract is accepted (they are not in the market yet). Under certain circumstances incumbents may therefore exploit contracting externalities to prevent entry (see Aghion and Bolton, 1987, Rasmussen et al., 1991, Innes and Sexton, 1994, Segal and Whinston, 2000b, Fumagalli and Motta, 2006, Simpson and Wickelgren, 2007, and Abito and Wright, 2008). The identi ed circumstances under which exclusive dealing can anticompetitively exclude rival incumbents are more restricted (see Mathewson and Winter, 1987, O Brien and Sha er, 1997, and, in particular, Bernheim and Whinston, 1998). 2 What is common in all of the above models is that product market competition takes place in a one-period game. The economic literature has therefore been concerned with the question of under which circumstances exclusive dealing may increase the static pro ts of a rm. Many recent antitrust procedures against exclusive dealing, however, have been concerned with another poten- 1 See Marvel (1982), Segal and Whinston (2000a), and De Meza and Selvaggi (2009) for e ciency justi cations of exclusive dealing. 2 Spector (2007) provides a synthesis of the di erent strands of the literature. 2

3 tial motivation to engage in exclusionary conduct: predatory exclusion of active rivals. Strong incumbent companies are sometimes accused of accepting lower pro ts in one period to exclude an incumbent competitor and recouping those losses in subsequent periods where monopoly rents can be earned. 3 Indeed, U.S. antitrust enforcement currently seems to consider only this second type of exclusive dealing as anticompetitive while typically not intervening against exclusive dealing of the sort discussed in the literature (which raises, rather than reduces current pro ts). One test that is considered in the U.S. is the pro t-sacri ce or no-economic-sense test (see Salop, 2006). This test checks whether an exclusive contract was consistent with (static) pro t maximization. If it is found that pro ts were sacri ced (and hence exclusive dealing made no economic sense from a static perspective), exclusive dealing is prohibited because it must have been predatory. If no pro ts were sacri ced, exclusive dealing may be allowed, in line with the Chicago School argument. 4 To our knowledge, predatory exclusive dealing has so far not been analyzed formally in the economic literature. This paper tries to ll this gap by investigating the ability of rms to use exclusive dealing in order to predate. Our model of predation loosely follows Bolton and Scharfstein (1990), who rst formalized the long-purse story of predation, according to which agency problems in nancial contracting may allow predatory pricing to exclude rivals. 5 By allowing for exclusivity clauses in a model of predation, we show that exclusive dealing may arise in equilibrium even in circumstances where it cannot be pro table for a one-period pro t 3 For a discussion of cases where exclusionary practices have been used by incumbents against rivals see for instance Spector (2007). 4 See Patterson (2003) for a discussion of antritust cases where the pro t-sacri ce test was applied. 5 In some sense, our paper takes the opposite perspective of Bolton and Scharfstein (1990). While their paper is detailed in its modeling of the nancial market, it is crude in the way it treats the product market. In particular, the price formation on the product market is not derived endogenously from a model of competition. Our paper, on the other hand, is detailed in the modeling of the product market while being crude in the treatment of the nancial market. In particular, the nancing constraints from the nancial market are not derived endogenously from a model of asymmetric information, but are assumed to be exogenous. 3

4 maximization strategy. Predatory exclusive dealing may not only be a possible strategy for dominant incumbents to exclude rivals; indeed, it is often a cheaper way of predating than predatory pricing. As shown below, this is the case if the prey s access to capital is not too limited, making ordinary price predation expensive. It also turns out that, the more market power the predator has with respect to the prey, the more likely it is that exclusive dealing is preferable for the predator compared to predatory pricing. Besides predatory pricing, other strategies of exclusion in a dynamic setup have been considered in the literature, under which rms trade o lower current pro ts for larger future pro ts. Carlton and Waldman (2002) describe how bundling can be used in a predatory way in evolving network industries. Ordover and Sha er (2007) show that rebate schemes can be used to exclude rival incumbents. The paper is organized as follows. Section 2 sets up the model. Section 3 characterizes the equilibria of a static game of exclusion, while Section 4 analyzes the equilibria of a dynamic game and presents the main results of the paper. Section 5 extends the model to a situation where rms can o er non-linear pricing schemes and Section 6 concludes. 2 The model The model combines the intuitions of Bolton and Scharfstein (1990) and Bernheim and Whinston (1998). Bolton and Scharfstein analyze a dynamic game of price competition in which exit may occur, but do not allow for exclusive dealing clauses. Bernheim and Whinston (1998), on the other hand, allow for exclusivity provisions, but consider only a static pricing game. 4

5 In our model, there are two upstream rms 1 and 2, each with xed costs F and marginal cost c, who compete in two periods = 1; 2. In each period, rms rst simultaneously announce whether they insist on exclusivity or not, as in Mathewson and Winter (1987). Afterwards they simultaneously set prices p 1 and p 2. 6 The products are purchased by a large number of identical downstream buyers who have preferences over the two goods which are given by Hotelling demand functions. Speci cally, each purchaser wants to buy a xed number of units in each period (normalized to 1) which he splits between rm 1 and rm 2. Each (marginal) unit x 2 [0; 1] gives purchasers utility u 1 tx if bought from rm 1 and utility u 2 t(1 x) if bought from rm 2, where t as usual denotes the degree of product di erentiation between goods 1 and 2. 7 As u 1 and u 2 may di er, we allow for vertical product di erentiation in addition to the horizontal di erentiation already inherent in the Hotelling model. Without loss of generality, let u 1 u 2 and denote u := u 1 u 2 0 as the degree of dominance of rm 1. 8;9 As usual in the Hotelling model, we will assume that u 1 and u 2 are su ciently large to ensure full market market coverage in equilibrium (speci cally, u i c + 2t for i = 1; 2). Moreover, let u < t, which implies that it is socially e cient that at least some units of rm 2 are sold (if it is active). The timing of the dynamic game is as follows. The game starts when both rms have sunk their xed costs in period 1. Firms then play the stage game described above, consumers make 6 In order to allow for the possibility of exclusion, we assume that rms cannot o er long term contracts but set prices in each period, as is common in models of predation. Note that rms pricing strategies are restricted to linear schemes in this section. In Section 5, we extend the analysis to non-linear pricing (two-part tari s). 7 Note the relation of this model to the standard Hotelling model. While in the latter there is a continuum of heterogenous consumers with unit demand, here purchasers are identical but have demand functions that are identical to aggregate Hotelling demand. One possible interpretation of our model is that purchasers are perfectly discriminating retail monopolists whose customers have Hotelling preferences over rms 1 and 2. 8 The legal de nition of dominance has typically been interpreted by economists as being equivalent to a high degree of market power or a low elasticity of demand. In our model u is indeed positively related to rm 1 s pro ts and negatively related to its elasticity of demand. 9 It would also be possible to introduce di erentiated marginal cost parameters. However, this a ects possible equilibria in the same way as di erentiated utility parameters. In order to save on notation, we therefore omit this type of di erentiation. The results can be easily reinterpreted to account for cost di erentials. 5

6 their orders and rst period pro ts are realized. If the rms expect non-negative pro ts in period 2 and have su cient funds to nance their ongoing operation, they remain in the market, and the stage game is repeated in the second period. If one rm exits the market after period 1 (a possibility that will be speci ed further below), this rm will not have to incur xed costs for period 2, and the other rm will be able to charge monopoly prices. Second period pro ts are discounted by some common discount factor, which we normalize to 1 for convenience. In line with Bolton and Scharfstein (1990), let one rm be the predator with su cient access to capital and the other rm be the prey, which is nancially constrained. Due to the assumption that u 1 u 2, rm 1 is the stronger rm in terms of market share in a standard one-period Hotelling game. It therefore makes sense to let rm 1 (the "dominant" rm) be the predator and rm 2 the prey. 10 We will assume that rm 2 does not obtain continued nancing by its investors if its pro t 2 falls below some threshold 2 in the rst period stage game. For instance, this constraint could represent Bolton and Scharfstein s (1990) argument that the weaker rm s nanciers face a problem of asymmetric information. If rst period pro ts turn out to be low, this may either re ect the fact that rm 2 is falling prey to a predator, or that rm 2 is less e cient than rm 1 and therefore cannot survive in the marketplace. As investors cannot distinguish the origin of the losses, they decide to withdraw their funding if pro ts are below 2. Firm 2 can always guarantee a pro t of F by not producing anything in period 1. A possibility for predation can therefore only arise if 2 F, which we will assume to be the case. In the other direction, it seems reasonable that the rm will not be shut down if it makes pro ts. We 10 In principle, however, it would be easy to extend our model to the case where the smaller rm has better access to nance. That said, predatory exclusion would become signi cantly less likely in the model, because the rst period costs of excluding a rival increase in the rival s market share. We therefore adopt the structure in the text, which appears empirically more relevant. 6

7 therefore have 2 2 [ F; 0], which we parameterize with 2 = F, (1) where the parameter 2 [0; 1] represents the leniency of rm 2 s banks. A value of = 0 means the banks are quite tough. Even if rm 2 breaks even, banks will shut it down. A value of = 1 on the other hand, means the banks are very soft. Only if rm 2 makes no sales at all it will be shut down; more moderate losses will be tolerated. We are now ready to solve the game by backward induction starting in period 2. This is essentially the case of static exclusive dealing as analyzed in the previous literature. 3 Exclusion in a static game There are two possible subgames that start in period 2. Either both rms are still active or rm 2 has been cut o from its funding after period 1 due to insu cient pro ts. If only rm 1 is active, it is easy to see that it charges the monopoly price p M 1 = u 1 t, leading to demand x M = 1, pro t M 1 = u 1 t c F and purchasers rent U M = 1 2t. Whether the rm announces exclusivity or not is irrelevant: there is no competition anyway. Next consider the case where both rms are still active in period 2. If nobody has announced an exclusivity requirement, the rms play the pricing game with Hotelling preferences, which we denote as regular pricing for later reference. Given p 1 and p 2 ; each buyer purchases x = p 2 p 1 + u 2t (2) 7

8 units of good 1 and 1 x units of good 2. The best response functions of rms 1 and 2 are therefore p 1 (p 2 ) = 1 2 (c + t + p 2 + u) and p 2 (p 1 ) = 1 2 (c + t + p 1 u). (3) This leads to a Nash equilibrium with p 1 = c + t + u 3 and p 2 = c + t u 3, so that x = u 6t, 1 = 1 2t t + u 3 2 F, 2 = 1 u 2 2t t 3 F, and the purchasers rent is U = 1 2 (u u 2 ) c 4 t + (u)2 36t. For later reference, note that rm 2 s one-period pro ts are non-negative if and only if F 1 2t t u 2. (4) 3 If one of the rms has announced an exclusivity requirement, downstream purchasers have to decide whether to exclusively buy from rm 1 or from rm 2. Sourcing from rm 1 generates a higher utility for purchasers if and only if p 1 p 2 + u. The only undominated Nash equilibrium in this subgame involves consumers choosing the dominant rm (x ED = 1) and rms choosing prices p ED 1 = c + u and p ED 2 = c. The proof for this equilibrium is analogous to the standard Bertrand game with di erentiated 8

9 cost, where u corresponds to the cost di erential. There is cut-throat competition, except for the cost advantage (here: utility advantage) of one of the rms. Therefore, it is costly to bribe purchasers into exclusivity. 11 The resulting equilibrium pro ts are ED 1 = u F and ED 2 = F, and the purchasers rent is U ED = u 2 c 1 2 t. As ED 2 < 2 for all parameter values, it is a dominant strategy for rm 2 not to require exclusivity. Since rm 1 is the stronger competitor, rm 2 can only lose any ght for exclusivity. For rm 1, however, exclusive dealing may or may not be pro table. Comparing ED 1 and 1 ; one nds that exclusive dealing is not pro table for rm 1 if and only if u 3 2 p 3 t. (5) Since 3 2 p 3 t 2 (0; t) ; this is a reiteration of Mathewson and Winter s (1987) result that exclusive dealing may occur in static games. In our model, exclusion in a one-period subgame arises if horizontal product di erentiation is small (t is small) but vertical product di erentiation is large (u is large). 12 For our purposes, this is just a reference point for later comparison. We will therefore now turn to the analysis of the rst period to characterize the scope of predatory exclusive dealing. 4 Exclusion in a dynamic game The previous section has shown that there are two circumstances under which exit of rm 2 can occur after period 1 even if rm 1 strictly maximizes one-period pro ts without sacri cing current 11 As in the Bertrand game with di erentiated cost, there exist additional Nash equilibria, which, however, involve the play of weakly dominated strategies by rm 2. Here, and in what follows, we will focus on undominated equilibria. 12 A cost advantage of rm 1 vis-à-vis rm 2 has an e ect equivalent to vertical product di erentiation. 9

10 rents to induce exit of rm 2. First, if condition (5) does not hold, rm 1 would opt for exclusivity in period 1 even if it (wrongly) expected rm 2 to stay in the market. As a consequence, rm 2 s pro ts fall below F; and it must close down. Second, if condition (4) does not hold, the competition under regular pricing is so intense that rm 2 cannot cover its xed costs of operation. In that case, rm 2 will voluntarily exit after period 1. Staying put would only in ict additional losses in period 2. These two outcomes can be described as exclusion by e ect because the implied strategies by rm 1 do not have the object of cutting rm 2 o from its funding. This is only the unintended e ect of a strategy that maximizes one-period pro ts. 13 The analysis of the overall game for these two cases is trivial. In period 1, both rms play the strategy that is optimal in a static game; rm 2 exits and rm 1 earns monopoly rents in period 2. Hence, we will now turn to the more interesting situation where conditions (4) and (5) hold, in which case exclusion is not pro table absent the intent to remove a competitor from the market. If exclusion occurs in this setting, then it is predation by object; that is, the willful sacri ce of current pro ts to earn future monopoly rents. 14 If future monopoly pro ts are su ciently high, some form of predation might be desirable for rm In order to decrease rm 2 s pro ts below the cuto threshold F, rm 1 may either propose an exclusive contract (predatory exclusive dealing) or it may forego exclusivity requirements but decrease its retail price below the level that is optimal from the viewpoint of 13 Notice that in principle, exclusive dealing may nevertheless cause damage to consumers. For instance, even in the case where consumers bene t in period 1 because rm 1 has to bribe them into exclusivity by o ering favorable conditions, they will incur future losses by facing a monopolist in period 2. That is, the question whether exit occured due to exclusive dealing (condition (5) does not hold) or whether it is a consequence of normal competitive pressure (condition (4) does not hold) may make a di erence for antitrust assessment. 14 In practice, the goal of predation may not always be virtual exit of the competitor. The predator may alternatively try to marginalize the prey by pushing it into a niche segment of the market or by making sure that the prey does not obtain the nancial resources to compete in the high-quality product spectrum. 15 Note that in our model (as in Bolton and Scharfstein, 1990) it can never be optimal for rm 2 to try to predate on rm 1. This follows from our assumption that rm 2 faces a nancial constraint, while rm 1 does not. Therefore, rm 1 will always be present in the second period, irrespective of what happens in period 1. 10

11 static pro t maximization (predatory pricing). The exclusive dealing strategy was outlined in the previous section. We therefore turn to predatory pricing now. Given p 1, rm 2 s optimal response p 2 (p 1 ) is given by (3). Plugging this into rm 2 s pro t function yields 2 (p 1 ) = (p 1 c + t u) 2 8t F. Setting this expression equal to F and rearranging gives the largest p 1 consistent with exclusion of rm 2, which is p P 1 = c t + u + p 8t(1 )F. As a result, the optimal price of rm 2 is given by p P 2 = c + p 2t(1 )F. This leads to x P = 1 q (1 )F 2t, P 1 = 1 q (1 )F 2t u t + p 8t(1 )F F, P 2 = F, and U P = 1 2 t. To determine the rst period outcome, there are therefore three potential equilibrium candidates: predatory pricing (leading to pro ts of P 1 + M 1 for rm 1), predatory exclusive dealing (leading to pro ts of ED 1 + M 1 for rm 1) and regular pricing (leading to pro ts of 2 1 for rm 1). The following proposition shows that all three outcomes can arise as equilibria of the dynamic game depending on the parameter values. So indeed it may be optimal for rm 1 to use an exclusive dealing contract to predate. However, it may also be the case that predatory pricing is a more pro table strategy for rm 1 or that neither of the two predatory strategies is pro table All proofs are contained in the appendix. 11

12 Proposition 1 Suppose that rms 1 and 2 compete in a dynamic pricing game. Then predatory exclusion may occur in period 1 if monopoly pro ts in period 2 are su ciently large. Depending on the parameters, exclusion either takes the form of predatory exclusive dealing or of predatory pricing. Exclusive dealing may occur even in a situation where exclusivity provisions cannot increase one-period pro ts. Given that both predatory pricing and predatory exclusive dealing can arise in equilibrium, the question is under which circumstances one or the other is preferable for rm 1. Proposition 2 provides a rst answer. Proposition 2 Suppose that future monopoly pro ts are su ciently large for some form of predatory exclusion to arise in period 1. Then, predatory exclusive dealing is more likely to occur if the nancing constraint of the prey is soft ( is large), while predatory pricing is more likely to occur if the nancing constraint of the prey is strict ( is small). This result re ects the main advantages and disadvantages of the two instruments. The big disadvantage of predatory pricing is that it forces rm 1 to decrease prices not only for marginal units (those that it intends to capture from rm 2 to force the latter s pro ts down), but also for intramarginal units. Predation is a costly exercise: the predator wants to enhance his reach, but this forces him to decrease prices. Exclusive dealing is less harmful in that respect. While it captures sales that would otherwise go to rm 2, it is easier to obtain pro ts on intramarginal units: At the equilibrium price under exclusive dealing, purchasers would prefer to source both from rm 1 and rm 2. However, the exclusivity clause prohibits that. Because no purchaser can obtain any units from rm 2, the choice is to purchase either all sales from rm 1 or none. Since 12

13 consumers do not want to forgo rm 1 consumption (especially if u is large), rm 1 can save some of the rents on intramarginal units. However, exclusive dealing is not without cost relative to predatory pricing. The big disadvantage of exclusive dealing is its scope. Exclusivity forces consumers to give up all of the consumer surplus that they would enjoy from sourcing some units from rm 2. This makes it costly to convince consumers to accept an exclusivity clause, especially if rm 1 s advantage u over rm 2 is only moderate. Predatory pricing does not su er from this disadvantage. In fact, it can be tailored to the degree of market exclusion that is necessary to induce exit of the prey. Indeed, if a small reduction of prices is su cient to push rm 2 into losses because the nancing constraints of rm 2 are tight, then bribing consumers into exclusivity would be far too expensive. Hence, predatory pricing is more attractive if banks are tough, while exclusive dealing is more attractive if banks are soft. The following proposition relates the foregoing discussion to the degree of dominance of the predator. Proposition 3 Suppose that future monopoly pro ts are su ciently large for some form of predatory exclusion to arise in period 1. Then, predatory exclusive dealing is more likely to occur if the degree of dominance u of the large rm is large, while predatory pricing is more likely to occur if the the degree of dominance u of the large rm is small. In light of the previous discussion, the intuition behind Proposition 3 is clear. If the predator is more dominant, then it would gain a large market share even if it did not predate. Bribing purchasers into accepting exclusion is less costly because the buyers do not regret losing access to rm 2 s products as much as would otherwise be the case. The cost of predatory pricing, on the 13

14 other hand, is relatively large in this scenario. Recall that its disadvantage is that prices are also reduced for intramarginal units. Since a dominant rm has many of those, it is more reluctant to use this instrument. Finally, we will relate the question of when predatory exclusive dealing occurs to a measure of rm 1 s optimal predatory price. Proposition 4 shows that a sharp distinction can be drawn to indicate under which circumstances exclusivity is pro table. Proposition 4 Suppose that future monopoly pro ts are su ciently large for some form of predation to arise in period 1. Then, predatory exclusive dealing will always be chosen if predatory pricing would involve below-cost predation (p P 1 c). Proposition 4 shows that rm 1 always prefers predatory exclusive dealing if predatory pricing is so costly that rm 1 has to lower its price below marginal costs to predate (p P 1 c).17 This is an interesting observation given the ongoing debate concerning whether or not above-cost predation should be prosecuted by antitrust law enforcement. 18 The prospect of predatory exclusion substantially alters the policy implications of exclusive dealing. For instance, Krattenmaker and Salop (1986) argue, based on models of exclusion in a static setting, that exclusionary practices should be prohibited only if they allow rms to raise prices. Matthewson and Winter (1987) support this standard and argue that the famous prohibition decision in Standard Fashion does not pass the test because exclusivity led to signi cant (short-term) price decreases for purchasers who accepted exclusivity. However, as the following 17 With di erentiated cost, below-cost predation can theoretically arise in our model. However, only if the predator is less cost e cient than the prey is this the case. If the predator has lower marginal costs than the prey, then below-cost predation can also be ruled out for di erentiated cost parameters. 18 For a discussion of above-cost predation see Edlin (2002) and Elhauge (2003), who disagree on the merits of such interventions. 14

15 proposition shows, predatory exclusive dealing always leads to price decreases as rm 1 has to convince consumers to give up sourcing from rm 2. The proposed antitrust standard would therefore imply per se legality of predatory exclusion, a recommendation that one may question. Proposition 5 If predatory exclusive dealing arises, then it leads to a price decrease relative to regular pricing in the rst period, (p ED 1 < p 1 ), but to price increases thereafter, (pm 1 > p 1 ). We will nish this section with some results on the welfare e ects of predatory exclusive dealing. These are summarized in the following proposition. Proposition 6 Compared to regular pricing, (i) predatory exclusive dealing reduces social welfare if and only if the xed costs of operation are su ciently small (F is small) and (ii) predatory exclusive dealing reduces consumer surplus if and only if consumers utility of purchasing the dominant rm s product is su ciently large (u 1 is large). As Proposition 6 shows, the welfare e ects of exclusive dealing are ambiguous. On the one hand, predatory exclusive dealing causes a distortion in product variety (there is no consumption of rm 2 s products which are foreclosed from the market). It is important to note, however, that regular pricing also leads to distorted product variety, even though there is no full exclusion: While under exclusive dealing purchasers obtain too many of rm 1 s products (1 instead of u 2t ), they obtain too few under regular pricing ( u 6t instead of u 2t ) as rm 1 exerts its market power by restricting quantity. Moreover, predation saves on future xed costs (along the lines of Mankiw and Whinston s [1986] argument of excessive entry). This explains the general ambiguity. Regarding consumer surplus, there is an additional trade-o. While predatory exclusive dealing leads to lower prices in period 1, it leads to higher prices in period 2. The latter e ect dominates 15

16 in the model whenever u 1 is su ciently large. In that case the second period monopoly price p M 1 = u 1 t is large and more than o sets the short-term exclusionary gains for consumers. 5 Non-linear pricing We will now analyze an extension of our basic model that allows for non-linear pricing as in O Brien and Sha er (1997). Consider a game that is equivalent to our previous set-up except that rms can now set two-part tari s. Therefore, each rm i chooses prices (L i ; p i ), where L i denotes a lump-sum charge and p i denotes a per-unit charge. As before, we will rst identify equilibria in the period 2 subgames. Suppose exclusivity has not been announced by any rm. If buyers purchase from both rms, x = p 2 p 1 + u 2t as before. But now there are two incentive constraints that ensure that it is optimal to purchase from both rm 1 and rm 2. The utility of purchasing from both must be larger than purchasing from either rm alone. Comparing the respective consumer surpluses for rm 1 (u(1; 2) u(2)) yields L 1 1 t p2 p 1 + u + t 2. (6) 2 Similarly, we have p1 p 2 u + t 2 (7) L 2 1 t 2 for rm 2. Both constraints must bind in equilibrium (otherwise, a rm could increase its pro ts by raising the xed fee). 16

17 Therefore, rm 1 chooses p 1 to maximize 1 = p 2 p 1 + u (p 1 c) + 1 p2 2t t p 1 + u + t 2 2 F where L 1 has been substituted from (6). This gives p 1 = c. Likewise, p 2 = c. Hence, x = u 2t, L 1 = 1 t t + u 2 2 and L 2 = 1 t t u 2 2 which leads to 1 = 1 t t+u 2 2 F and 2 = 1 t t u 2 2 F. Note that 2 0 if and only if u t 2 p tf (8) which we will again assume to hold. Otherwise exit of rm 2 would automatically occur after period 1. Next we will investigate the subgame where one of the rms has announced an exclusivity requirement. In this case, buyers will purchase the measure one units from either rm 1 or rm 2. As the volume is xed, the structure of the payment ( xed or variable) is irrelevant; only the total level matters. Hence, without loss of generality, we can set p ED 1 = p ED 2 = c. Buyers will purchase from rm 1 if and only if L 1 L 2 + u. With the previous Bertrand argument, this leads to equilibrium fees of L ED 1 = u and L ED 2 = 0. 17

18 Firm 2 will always be excluded in this subgame, i.e. x ED = 1. Therefore, ED 1 = u F and ED 2 = F. It is easy to see that ED 2 2. Therefore, rm 2 will never announce exclusivity in period 1. Exclusive dealing will be more pro table for rm 1 ( ED 1 > 1 ) if and only if (u t) 2 < 0, which cannot be the case. Hence, exclusive dealing will never be used, and regular pricing is the relevant subgame in the subgame perfect Nash equilibrium of the overall game. This result contrasts with the result of Section 3: If rms can employ two-part tari s exclusion can never be pro table in a one-period game. This is in line with O Brien and Sha er (1997) and Bernheim and Whinston (1998), who show that Mathewson and Winter s (1987) result is reversed if non-linear pricing schemes are taken into account. Essentially, these results restore the logic of Bork (1978) that rms cannot increase their pro ts through exclusivity provisions. But while exclusive dealing is not pro table in a static environment, it may still be the case that it is a useful instrument to predate on competitors. This would rationalize the view held by some observers that exclusive dealing should only be questioned by competition authorities if it can be shown to be predatory. Assume period 2 pro ts are su ciently large for some form of predatory exclusion to be optimal. Exclusive dealing is one possible strategy to predate. The equilibrium of this subgame was described above. Next consider price predation. As p 2 = c is optimal for rm 2 irrespective of rm 1 s choice of price schedule, its optimal xed fee depending on p 1 can be inferred from (7) 18

19 as p1 c u + t 2. L 2 = 1 t 2 This yields pro ts of p1 c u + t 2 F. 2 = 1 t 2 In order to predate, these pro ts have to be pushed down to F. This occurs if p P 1 = c + u t + 2 p t(1 )F. (9) Therefore L P 1 = t 2 p t(1 )F + (1 )F, x P = 1 q q (1 )F t, and P 1 = u F + (1 )F t (t u) (1 ) F. Comparing ED 1 and P 1 then yields the following proposition. Proposition 7 Suppose that rms 1 and 2 compete in a dynamic pricing game with two-part tari s. Then, neither of the two rms will impose an exclusivity requirement on purchasers. In other words, there is a one-to-one relationship between the environment that allows exclusion to be pro table in a one-period setup and the environment that allows exclusion to be pro table in a dynamic setting. In the logic of Bernheim and Whinston (1998), exclusive dealing can only be pro table in the absence of e ciency motives if there are contracting externalities. As shown in Sections 3 and 4, one such imperfection is the case where rms are restricted in setting non-linear tari s. 19 While Proposition 7 (and the previous results by O Brien and Sha er, 1997, 19 The argument readily extends to the case where rms can use two-part tari s, but can only increase xed fees up to some limit L, perhaps for fear of antitrust prosecution of price discrimination. It is easy to show that predatory exclusive dealing is pro table for rm 1 provided that L is not too large. 19

20 and Bernheim and Whinston, 1998) calls for caution in marking exclusivity provisions as anticompetitive, there are at least two important reasons why the situation depicted in the previous sections, where predatory exclusive dealing could arise, are relevant in practice. First, the assumption of two-part tari s with full knowledge of the demand curves of individual purchasers is clearly extreme. Perfect price discrimination of the sort assumed in this section, which allows full extraction on residual demand curves, is typically not observed in the real world. However, once marginal cost pricing on incremental units cannot be maintained (say, because rms do not know purchasers individual demands with certainty), we again enter a world with contracting externalities. As Spector (2007) notes, nonlinear pricing together with asymmetric information resembles linear pricing. We are therefore back in the scenario of Proposition 7; that is, predatory exclusive dealing may occur. Second, even if rms possess the large informational requirements leading to Proposition 6, they may still prefer exclusive dealing over predatory pricing because it is less easily detectable as a predatory strategy. This is shown in the following proposition. Proposition 8 Suppose that rms 1 and 2 compete in a dynamic pricing game with two-part tari s. Then predatory pricing always involves below-cost predation (p P 1 < c), while predatory exclusive dealing can always be carried out with above-cost predation (p ED 1 c). As a result, competition authorities may be able to infer predatory pricing from cost observations if rms use non-linear pricing schemes. Predatory exclusive dealing, on the other hand, can always be carried out with incremental prices above cost. Thus, it is likely to be more di cult for a competition authority to actually prove that the predator has sacri ced pro ts by o ering exclusive contracts. 20

21 In summary, we believe that the result of Proposition 7 should be seen as pointing to the necessary conditions for predatory exclusive dealing to arise, rather than ruling it out as a matter of principle. In the limiting case of full information and perfect non-linear pricing, predatory exclusive dealing will not arise. However, in a less than perfect world, the intuition of the main body of our paper again provides the relevant framework of analysis. 6 Conclusion This paper has introduced exclusivity clauses into a model of predation along the lines of Bolton and Scharfstein (1990). As a result, two distinct forms of predatory exclusion arose in equilibrium, which are also observed in practice: predatory pricing and predatory exclusive dealing. Exclusive dealing can be a pro table strategy to exclude rivals with nancing constraints, even in circumstances where exclusive contracts can never be pro table from the perspective of static pro ts. The more market power a predator has on the product market, the more likely it is that predatory exclusive dealing is a more pro table exclusionary strategy than predatory pricing. The previous literature on exclusive dealing has concluded that the exclusion of existing competitors (as opposed to abstract potential entrants) can only have anticompetitive e ects under particular conditions - for instance, if there are contracting externalities from related markets (see Bernheim and Whinston, 1998, and Whinston, 2006). This paper, in contrast, has argued that the scope for anticompetitive exclusive dealing is much larger. While exclusive dealing may often not be pro table in a static context, it may provide a cheap and e ective instrument of predation. Our model (and the related work by Mathewson and Winter, 1987, O Brien and Sha er, 1997, and Bernheim and Whinston, 1998) has assumed that downstream purchasers are either nal consumers or local monopolists, who do not compete with each other. It would be interesting to 21

22 extend the present analysis to downstream competition. Fumagalli and Motta (2006) and Simpson and Wickelgren (2007) have shown that the e ect of downstream competition on the potential for exclusion is ambiguous for the case of potential entrants. Extending their work to the exclusion of competing incumbents seems to be a promising direction for future research. 22

23 7 Appendix Proposition 1: Proof. Suppose that u 1 is large (which implies that period 2 monopoly pro ts M 1 are large). We will prove that in this case, rm 1 will always nd it optimal either to engage in predatory pricing or to impose exclusivity. Consider rst the situation where rm1 has not imposed exclusivity before the pricing game in period 1. In this case two equilibrium candidates remain. For rm 1, the predatory pricing outcome is more pro table if and only if P 1 + M (10) Substituting the appropriate values from the text in (10) and rearranging yields 1 r (1 ) F 2t! u t + p 8t (1 ) F + u 1 t c 1 t + u 2. (11) t 3 Holding u constant, (11) must clearly hold for su ciently large u 1. I.e., if the prospect of future monopoly pro ts is su ciently large, rm 1 will nd it optimal to predate in the absence of exclusive dealing. In this situation, however, it may be more pro table for rm 1 to impose an exclusivity requirement in the rst place. This is the case if and only if ED 1 + M 1 P 1 + M 1. (12) 23

24 Substituting the appropriate values from the text in (12) and rearranging yields u s 2t (1 ) F 1! t + p 8t (1 ) F. (13) What needs to be shown is that (13) may or may not hold, depending on the value of parameters (within the parameter restrictions of the model). To show that exclusivity may be pro table, let! 1. In this case the right-hand-side of (13) converges to 1, and so (13) clearly holds. Next, to show that exclusivity may not hold, let u = 0, = 0, and F = t=2. 20 In this case (13) is equivalent to 0 t (14) which cannot hold. Hence, in this case it is preferable for rm 1 not to impose exclusivity and to predate in the pricing game. I.e., for su ciently large u 1, rm 1 will either engage in predatory exclusive dealing or predatory pricing, depending on parameter values. Proposition 2: Proof. Note that in (12), the only term that is a function of is P 1. To prove that predatory pricing becomes relatively less pro table compared to exclusive dealing as increases, we therefore have to P = r s 2tF F + (u t) 1 8 (1 ) t + 2F < 0 which is equivalent to 1 4 (u t) + p 2 (1 ) tf t < 0. (15) 20 Note that these parameter values are consistent with the restrictions imposed by the model setup. In particular, they are consistent with inequality (4). 24

25 We know the rst term in (15) to be negative. p 2 (1 ) tf t 0 if and only if t 2 (1 ) F. (16) This is most di cult to ful ll in case = 0, in which case (16) reduces to F t 2. (17) (17) however must hold given (4), so we can indeed conclude that (15) holds, which proves the proposition. Proposition 3: Proof. From (13) it immediately follows that, ceteris paribus, exclusive dealing becomes relatively more attractive if u increases. Proposition 4: Proof. Suppose p P 1 predatory pricing P 1 < c. In that case it must be that rm 1 s rst period pro ts under F ( rm 1 not only has to come up for xed costs, but incurs additional losses on every sold unit due to below cost pricing). However, we know from Section 3 that rm 1 s rst period pro t under exclusive dealing is equal to ED 1 = u F. Hence, we have ED 1 = u F F > P 1, which proves the proposition. Proposition 5: Proof. First, we will show that p ED 1 < p 1. Substituting the appropriate values from Section 3 and rearranging yields u < 3 (c + t + F ). (18) 2 25

26 We know from Section 2 that the left-hand side of (18) is smaller than t. As the right-hand side is larger than t, (18) must hold which proves the rst part of the proposition. Second, we will show that p M 1 > p 1. Substituting the appropriate values friom Section 3 and rearranging yields u 2 > t F. (19) We know from Section 2 that the left-hand side of (19) is larger than c + 2t. As this value exceeds the right-hand side of (19), (19) must indeed hold, which proves the proposition. Proposition 6: Proof. In case of exclusive dealing, rst period welfare is equal to W ED 1 = u 2 c 2t+u 2F. Second period (monopoly) welfare is equal to W M 1 = u 1 2t c F. Adding the two gives a two-period welfare of W ED + W M = u 1 + u 2 2c + u t 3F. (20) One period welfare under regular pricing, by contrast, is equal to W = 1 2 (u 1 + u 2 ) c 1 4 t + 5 (u) 2 36 t 2F, which means that two-period welfare is equal to 2W = u 1 + u 2 2c 1 2 t + 5 (u) 2 18 t 4F. (21) Comparing (20) and (21) and rearranging shows that exlusive dealing reduces welfare if and only if F 1 2 t + 5 (u) 2 18 t u. (22) Comparing this threshold for F with the threshold of admissible values of F de ned by (4) shows that the former is stricter than the latter. Hence, for small values of F welfare is decreased as a 26

27 result of exclusive dealing, while for larger (but still admissible) values of F it is increased. Next consider consumer surplus. In case of exclusive dealing rst period consumer surplus is equal to U ED 1 = u 2 c 2 t. Second period (monopoly) consumer surplus is equal to U M = 1 2t. Adding the two gives U ED + U M = u 2 c. (23) One period consumer surplus under regular pricing, by constrast, is equal to U = 1 2 (u 1 + u 2 ) c 5 4 t (u) 2 t, which means that two-period consumer surplus is equal to 2U = u 1 + u 2 2c 5 2 t (u) 2. (24) t Comparing (23) and (24) and rearranging shows that eclusive dealing reduces consumer surplus if and only if u 1 c 5 2 t + 1 (u) 2 18 t 0. Hence, for large values of u 1 consumer surplus is reduced by exclusive dealing, while for smaller (but still admissible) values of u 1 it is increased. Proposition 7: Proof. Comparing 1 ED and 1 P and rearranging yields that exclusive dealing is more pro table if and only if u > t p t (1 ) F. (25) The right hand side of (18) is larger than the right hand side of (8), therefore (18) cannot hold. Hence, Predatory pricing must yield higher pro ts than predatory exclusive dealing. 27

28 Proposition 8: Proof. From (9), p P 1 < c if and only if u < t 2 p t (1 ) F. (26) The right hand side of (26) is larger than the right hand side of (8), therefore (26) always holds. Moreover, as pointed out in Section 5, the incremental price p ED 1 = c is part of an equilibrium in the exclusive dealing subgame; that is, p ED 1 < c can always be avoided. 28

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